انتصار عبد الحر كاظم العيساوي

In this paper 3-soft prime ideals and 3- soft prime ideal near ring are defined and their basic algebraic characterization are studied. Also we identified some related properties of these soft substructures.

In this paper, we introduced the notion of cubic AB-ideals in AB-algebras with its properties that are investigated. Moreover, the image of cubic AB-ideals in AB-algebras and its inverse had been defined.

In this paper ,we introduce the notions 3- prime ideal with respect to an element x denoted by (x-3-prime ideal ) of a near ring and the 3-prime prime ideal near ring with respect to an element x denoted by (x-3-prime ideal near ring ) ,and we studied the image and inverse image of x-3-prime ideal under epimomorphism and the direct product of x-3-prime ideal of near ring .

The group of all Z-valued characters of a finite group G over the group of induced unit characters from all cyclic subgroups of G forms a finite a belian group, called Artin Cokernel of G ,denoted by AC(G).The problem of finding the cyclic decomposition of Artin cokernel has been considered in this paper ,the cyclic decomposition of D2n x C3 is : AC( D2n x C3 )=+1-2n(C2) Also we give the general form of rational character and Artin's characters tables of group D2n x C3

The group of all Z-valued characters of afinite group G over the group of induced unit characters from all cyclic subgroups of G forms a finite a belian group, called Artin Cokernel of G ,denoted by AC(G).The problem of finding the cyclic decomposition of Artin cokernel AC(D2nh)has been considered in this paper, , the cyclic decomposition of AC(D2nh) is : AC(D2nh) =+ C2 . And we give the general form of Artin's characters table Ar(D2nh).